Addition of Frequencies: Combining Same Phase, Different Amplitudes

[henil]

i want to add two frequencies having same phase but different amplitudes, in what manner i can proceed ?

 

[fresh_42]

If you have two amplitudes $a_1, a_2$ and the same phase $φ$ then your waves are $a_ 1 \sin{φ}$ and $a_ 2 \sin{φ}$ so the resulting wave is $(a_1 + a_2) \sin φ$.

 

[sophiecentaur]

i want to add two frequencies having same phase

The phases of any two signals with different frequencies will coincide momentarily at a rate equal to the difference in the frequencies
but they cannot 'have the same phase'. You can, of course, choose your time origin to be when the phases of both signals are both zero. This would make the starting equation simpler.
Could it be that you are adding two signals with the same frequency.